A typical computer network, such as an internet protocol (IP) network, supports communications between various network devices. When two network devices communicate, the devices establish a communication session using a communication protocol, such as the Transmission Control Protocol (TCP). Devices, such as routers and switches, forward packet flows associated with the communication session through the physical network that connects the devices. Each TCP session, for example, typically includes two packet flows in opposite direction between the devices. Each flow of packets between the devices for a TCP session is commonly referred to as a TCP flow or a TCP stream. The devices may provide quality of service (QoS) to TCP sessions to reduce latency, delay, or jitter in communications between the devices. For example, the devices may assign priority among multiple TCP sessions.